Best Known (86−71, 86, s)-Nets in Base 7
(86−71, 86, 23)-Net over F7 — Constructive and digital
Digital (15, 86, 23)-net over F7, using
- net from sequence [i] based on digital (15, 22)-sequence over F7, using
(86−71, 86, 48)-Net over F7 — Digital
Digital (15, 86, 48)-net over F7, using
- t-expansion [i] based on digital (13, 86, 48)-net over F7, using
- net from sequence [i] based on digital (13, 47)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 13 and N(F) ≥ 48, using
- net from sequence [i] based on digital (13, 47)-sequence over F7, using
(86−71, 86, 149)-Net in Base 7 — Upper bound on s
There is no (15, 86, 150)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(786, 150, S7, 71), but
- the linear programming bound shows that M ≥ 3 427795 996962 229821 860607 651257 847081 736828 639336 458852 541203 433121 888871 909785 796350 220666 781245 240401 184328 079725 562376 439362 027481 124622 202358 371384 427600 541903 910614 192771 966626 069100 043651 516512 969662 106512 / 698871 027983 609063 992761 952350 527056 373302 806763 499393 142870 103567 784157 462656 917651 129256 039318 757114 462936 082132 357258 750078 707671 168993 > 786 [i]